It's a bit like asking whether cats are better than dogs. If you want to shout, "Here Rover!" and go for five mile walks in the rain, I guess you are not a cat person.
John Gay was an opportunist, who took advantage of the fact that copyright laws (if they existed at all) were regarded in a relaxed manner. He wrote an improbable, but entertaining story. That was his only (artistic?) ambition.
Our Bert was a very different animal. His aims were far more ambitious and he was conscioulsy didactic. I like his burning wit and irony, but I guess it isn't for everyone.
Interestingly enough, although it was a box office success, Brecht himself regarded it as essentially a failure. He felt that his didactic intentions were being overlooked by the audience. Two years later, he collaberated (with Weill again I think, but I don't have time to look it up) on Mahagonny. Nobody could possibly miss the blunt intentions of that play. Crude as it is, I prefer it. I believe most Mudcatters would recognise the song, "Show Me The Way To The Next Whisky Bar" from it.
Brecht was a vain,devious and arrogant man.(He did not even learn to speak English during his years of exile in the US, which certainly saved his life). He could write a bit though!